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Questions tagged [optimization]

Optimization is the process of choosing the "best" value among possible values. They are often formulated as questions on the minimization/maximization of functions, with or without constraints.

In mathematics, computer science, economics, or management science, mathematical optimization (alternatively, optimization or mathematical programming) is the selection of a best element (with regard to some criteria) from some set of available alternatives.

An optimization problem can be represented in the following way: given a function $f:A\to\mathbb{R}$ from some set $A$ to the real numbers, we want to find an element $x_0\in A$ such that $f(x_0)\le f(x)$ for all $x \in A$ ("minimization") or such that $f(x_0)\ge f(x)$ for all $x \in A$ ("maximization").

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Find max/min values of the sum of squares

How to find max/min values for the sum of squares: $n_1^2 + n_2^2 + ... + n_i^2$ where $n_1 + n_2 + ... + n_i = c$ Is it true that max value is always obtained when $n_1 = n_2 = ... = n_i$?
user39086
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Dynamic or virtual Queue

I am trying to formulate one equation. Let $Q(t)$ represent the contents of a single-server discrete time queueing system defined over integer time slots $t \in \{0, 1, 2, . . .\}$. Specifically, the initial state $Q(0)$ is assumed to be a…
Sabbir Hasan
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Framing a travelling salesman problem

I have an optimization(optimisation) problem, I think it is travelling salesman, where I want to find an answer to the question: "What is the best coffee shop for person x within a 50km radius?" The variables for this question are dependent on:…
Seth
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Adding a constant to a list of numbers so that the sum of distances to integer values is minimal

I have a list of numbers {$x_i$} and I want to shift them (add a constant $\delta$) so that they are as close as possible to integer numbers in the sense that the summed distance to integer numbers gets minimal. $D=\sum |y_i - round(y_i)|$ minimal…
NoDataDumpNoContribution
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Lagrangian step for optimizing a concave function

I finding some difficulties in solving the below constrained problem using Lagrangian. Would be great if some one helps me with the steps. $\min_C \sum_i \Psi(c_i)$ subject to $\sum_i c_i = 1$ and $c_i \geq 0$ for $i=1 \cdots k$ and $C=[c_i]$ Here…
Learner
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Optimization Software

I am currently trying to optimize an equation that contains 4 variables. It is nonlinear and non-convex. In mathematica, to optimize this equation, I take the partial derivative of each variables, then set it to zero and solve it together. It is…
kuku
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Minimizing sum of functions implies minimizing their squares, maximizing the sum of the inverses?

I have $n$ functions (Say $f_1\space to \space f_n$) of $k$ variables (Say $x_1\space to\space x_k$) each. The functions are all positive, as well as the variables $xi's$. I do not have explicit expressions for these functions. The objective is to…
Hussein Hammoud
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KKT Condition : Always either a Maxima/minima or Saddle?

For a constrained optimization problem, in general the KKT conditions are a necessary but not sufficient condition for a point to be the local maxima/minima of the objective function. Is it always true that if the point is not a local maxima/minima,…
Optimized Life
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minimization with many unknowns and one condition

I haven't done this in quite a while so excuse my perhaps silly question. I'm looking for a solution to a minimization problem (if there is one), that goes like this: I want to minimize (global) $f(x,y,z)=x^2+y^2+z^2$ under the condition that…
egg
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Lagrangian method gives the wrong answer in a standard constrained optimization problem

I had this strange problem where the Lagrangian method gives the wrong answer in a constrained optimization problem. Here goes: The problem is $$\max_{c,n,q} \alpha\log(c)+(1-\alpha)\log(nq)$$ subject to $$c+n+nq=1 \text{ and }c,n,q\geq 0$$ where…
oopsroger
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To minimize $x^TAx$ where $A$ is not necessarily positive semi-definite with constrains?

Let $A\in \mathbb{n\times n}$ be a symmetric matrix. Let $x\in \mathbb{R}^{n\times 1}$ be an unknown vector. The problem is $$\min \limits_x \{E(x)=x^TAx\}$$ where $x\in C$, $C$ is a convex set. $C=\{x|\sum\limits_i^n x_i=0\}$. Is there any way…
user18481
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Find the minimum of $x^{2}+5y^{2}+8z^{2}$ if $xy+yz+zx=-1$

If $xy+yz+zx=-1$，find the minimum of $x^{2}+5y^{2}+8z^{2}$. How to solve it use Elementary mathematics methods？
tianzhidaosunyouyu
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Which optimization can I use: Hill climbing, simulated annealing, or ant colony algorithms?

I plan to make program to carry out optimization. In my optimization problem, there are three parameters, for instance $X$, $Y$, $Z$, that must be optimized (or minimized in this case since all the values of $X$, $Y$, $Z$ must be as low as…
user1221330
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easy explanation of Newton's method

I was reading a tutorial of training a neural network using Newton's method and it says, "The maximum error reduction (of the error surface function) depends on the ratio of the gradient to the curvature. So, a good direction to move in is one with…
DSKim
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What is this problem called?

I don't know the name of this problem, but I heard it some time ago. The statement was if a planet is distance $d$ away, and you know both the current maximum velocity of spaceships $v_0$ and the growth rate of spaceship propulsion technology $a$…
Teofrostus
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